I am just thinking about why this is true. Can I change it to
Q1. If a series is convergent then the series can be regrouped without changing the order of terms.
For example the sum of $(-1)^n$ is an alternating sequence and it is divergent, so I can't regroup them?
Q2. Can I claim that a convergent, non-alternating series be absolutely convergent?
As there is no difference after the term become absolute value, it should be still convergent after absolute those terms?
Q3. What does conditionally convergent mean? If a sequence is either convergent or absolutely convergent then it is conditionally convergent?